You can get to downtown Los Angeles by public transportation, which may be your best bet during the week to beat traffic. On weekends, take advantage or lower rates at the downtown Los Angeles hotels, get some tickets for a performance at the Music Center and leave the car in the parking garage until you're ready to go home.
Despite the city being so large, downtown Los Angeles is relatively small, and the average walker can see much of it on foot. Besides sparing your mood from parking hassles, walking allows you to see more and explore. If you get tired, the DASH bus system covers most of the area described on this tour. Their routes are different on weekdays than weekends, and their prices extremely reasonable (50 cents per ride in late 2013).
If you'd like an audio companion as you explore downtown, try the free MP3 podcasts offered by the Los Angeles Conservancy or Downtown L. A. Walks. For the history or architecture-lover, the Los Angeles Conservancy also offers guided walking tours on a weekly basis, but reservations are required.
DowntownLA.com also has a lot more information than we've given you here.